Partial and total photoionization cross sections of the K shell of the N-2 molecule are calculated using the generalization of the random-phase approximation that has been applied earlier to the valence shells of N-2 [Phys. Rev. A 61, 032704 (2000)]. At zero order the relaxed core Hartree-Fock approximation is used. It is demonstrated that due to strong intershell correlations the sigma* shape resonance reveals itself not only in the 1sigma(g)-->epsilonsigma(u) channel as it takes place in all single-particle approximations, but also in the 1sigma(u)-->epsilonsigma(g) channel. The influence of vibrational motion on the cross sections is taken into account. Good agreement with the most recent experimental data for different partial cross sections is achieved.
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